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The remainder when the positive integer
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20 Jun 2020, 06:44
20 Jun 2020, 06:44
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The remainder when the positive integer \(m\) is divided by \(n\) is \(r\). What is the remainder when \(2m\) is divided by \(2n\)?
A) \(r\)
B) \(2r\)
C) \(2n\)
D) \(m - nr\)
E) \(2(m - nr)\)
A) \(r\)
B) \(2r\)
C) \(2n\)
D) \(m - nr\)
E) \(2(m - nr)\)
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The remainder when the positive integer
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20 Jun 2020, 09:44
20 Jun 2020, 09:44
1
asifbinsyed33 wrote:
The remainder when the positive integer \(m\) is divided by \(n\) is \(r\). What is the remainder when \(2m\) is divided by \(2n\)?
A) \(r\)
B) \(2r\)
C) \(2n\)
D) \(m - nr\)
E) \(2(m - nr)\)
A) \(r\)
B) \(2r\)
C) \(2n\)
D) \(m - nr\)
E) \(2(m - nr)\)
There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
------NOW ONTO THE QUESTION------------------------
The remainder when the positive integer m is divided by n is r.
We're not told the quotient here (i.e., the Q value), so let's say the quotient is k
In other words, "m is divided by n equals k with remainder r."
We can write: m = nk + r
What is the remainder when 2m is divided by 2n ?
If m = nk + r, then 2m = 2(nk + r)
Expand to get: 2m = 2nk + 2r
Or we can say: 2m = (k)2n + 2r
This tells us that 2m is 2r greater than some multiple of 2n. So if we divide 2m by 2r, the remainder must be 2r
Answer: B
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Re: The remainder when the positive integer
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09 Jul 2021, 08:39
09 Jul 2021, 08:39
1
Theory: Dividend = Divisor*Quotient + Remainder
The remainder when the positive integer \(m\) is divided by \(n\) is \(r\)
m -> Dividend
n -> Divisor
q -> Quotient [assume]
r -> Remainders
=> m = n*q + r = nq+r ...(1)
What is the remainder when \(2m\) is divided by \(2n\)
Multiply (1) *2 we get
2m = 2nq + 2r
This means, 2m when divided by 2n gives q as quotient and 2r as remainder
So, answer will be B
Hope it helps!
To learn more about Remainders, watch the following video
The remainder when the positive integer \(m\) is divided by \(n\) is \(r\)
m -> Dividend
n -> Divisor
q -> Quotient [assume]
r -> Remainders
=> m = n*q + r = nq+r ...(1)
What is the remainder when \(2m\) is divided by \(2n\)
Multiply (1) *2 we get
2m = 2nq + 2r
This means, 2m when divided by 2n gives q as quotient and 2r as remainder
So, answer will be B
Hope it helps!
To learn more about Remainders, watch the following video
